Caution ahead of the Q3 corporate earning session starting this week and outcome of the ongoing US-China trade talks kept the indices in a short range.
The Asian markets also traded on a mixed note.
The key finance stocks traded 0.04 per cent lower while power, oil and gas, metal scrips also declined.
In contrast, the banking stocks gained.
The S&P BSE Sensex opened at 35,964.62 from its previous close of 35,850.16 on Monday.
At 10.45 a.m., the Sensex traded 70.20 points or 0.20 per cent higher at 35,920.36.
The Nifty of the National Stock Exchange (NSE) opened at 10,786.25 after closing at 10,771.80 on Monday.
The Nifty traded at 10,792.05 during the morning trade session, up 20.25 points and 0.19 per cent.